simple pictures, tough problems

[Steve Lehar]

> The   nice  hierarchical   classification  of   simple, complex,   and
> hypercomplex  cells has    been   assaulted   for  two  reasons:   the
> hypercomplex    category  is   questionable,  and  the   hierarchy  is
> questionable.

We observe in the visual cortex  many different cells, some respond to
very simple  features,  others to  more   complex  features, others to
hypercomplex- Ahem!  Excuse me-  Even more complex  features and so on
upwards through   the  temporal lobe  to cells  that respond   to very
complex specific  stimuli.   Are you suggesting  that the most complex
cells do not take their  input from the  intermediate level cells, but
compute their  response  directly  from  the   raw input from  lateral
geniculate?  I find this most unlikely!  What would  be the purpose of
all those intermediate level representations if not for the use of the
higher level  cells?   And why   do  we  find ascending complexity  of
representation in a continuous spatial progression?  Why would  we not
find very high  level cells mixed in  with simple  cells at V1 if they
compute their responses  independantly to the  intermediate levels  in
V2, V3...?

> There is evidence that the processing by simple and complex cells take
> place  at least  partially in parallel.  

So is your complaint that the visual hierarchy is not a PURE hierarchy
because certain connections  jump from low levels to  very high levels
bypassing intermediate levels?  You will find no  argument from  me on
that matter.  I would assume however that most  high level cells would
also take input from intermediate levels, so we have a mixed hierarchy
with  lots  of connections everywhere,  but a  hierarchy nevertheless!
The  spatial arrangement of  cortical regions  alone strongly suggests
that to be the case.  My argument about the spatial/featural transform
at each  stage  holds for a  mixed  hierarchy as it does  for   a pure
hierarchy.  The evidence for this seems  overwealming- that the higher
the  cell is  in the hierarchy, generally the  larger is the region in
the visual field to which it will respond.  This is what I mean by the
spatial/featural  hierarchy, that  every    stage  in   the  hierarchy
increases featural  specificity  while decreasing spatial specificity.
And I maintain  that it is that  aspect of the  hierarchical structure
which  lends the property of spatial  generality which is  so  hard to
achieve in conventional recognition algorithms.

> Even a  parallel  system evolves   through   time.  We   can treat the
> vibration  of a  violin string as  proceding  in discrete  time if our
> sampling rate is high  enough (for bandlimited behavior).  Each moment
> of this discrete  time constitutes  an iteration.  To the extent  that
> the time constant of a biological neural network's behavior is finite,
> we _do_ have  to worry about  how many iterations (how  much time)  it
> takes for the system to arrive at a solution.

I  did  not mean   to   suggest  that   resonance  can be  established
instantaneously, of course it requires  a finite time.  I merely meant
to  say that in  the case of resonance,  a causal order (bowing causes
string to resonate) does not necessarily imply a temporal order (first
bowing then resonance)  but that the  resonance can emerge essentially
simultaneous to the bowing, even though the bowing is the cause of the
resonance.  In the same  way, I suggest that the  fact that  a  higher
level cell  fires before  the lower level  cell, does  not necessarily
imply that it is therefore causally independant.  

Of  course by firing I  mean firing  above ambient  noise level, and I
would assume  that there  is some a  signal being sent from the  lower
level cell  to the higher  one,  albeit a weak,   noisy and incoherent
signal, and that the higher level cell responds to and accentuates any
global coherency that it detects in the cacophany of noisy inputs that
it receives  from many lower  cells.   The BCS model suggests that the
output of the lower level cell is greatly boosted and enhanced when it
receives top-down confirmation, or suppressed  if it receives top-down
disconfirmation, thus a global pattern detected higher up is reflected
in the pattern of firing in the lowest levels of the hierarchy.  It is
this stronger, resonant firing of the low level cell that occurs AFTER
the higher  cell  response, the  initial firing might  be  lost in the
noise.

This arrangement seems  eminantly plausible to  me, accounting  for  a
large body of psychophysical data including  the ease with which local
objects are  recognized  when they are    consistant with  the  global
picture, and conversely, the longer time required to recognize objects
that are  inconsistant with the  global scene.  It  is clear  that the
global  context plays  a large role in local  recognition, although of
course the global context itself must be built up out of local pieces.
How else can  one account for these  phenomena besides  a simultaneous
resonant matching between low and high level recognition?